What is the dimension of citation space?

TL;DR

This paper introduces novel methods to measure the causal structure dimension of citation networks, revealing differences linked to diversity in citation behavior across various domains.

Contribution

It adapts quantum gravity causal set methods to analyze citation networks, providing a new quantitative approach to understand their underlying structure.

Findings

Citation networks have measurable dimensions that vary across domains.

Differences in network dimensions relate to diversity or narrowness in citation patterns.

Methods can distinguish between different types of citation networks based on their causal structure.

Abstract

Citation networks represent the flow of information between agents. They are constrained in time and so form directed acyclic graphs which have a causal structure. Here we provide novel quantitative methods to characterise that structure by adapting methods used in the causal set approach to quantum gravity by considering the networks to be embedded in a Minkowski spacetime and measuring its dimension using Myrheim-Meyer and Midpoint-scaling estimates. We illustrate these methods on citation networks from the arXiv, supreme court judgements from the USA, and patents and find that otherwise similar citation networks have measurably different dimensions. We suggest that these differences can be interpreted in terms of the level of diversity or narrowness in citation behaviour.